Question
Convert 1 Joule of energy into CGS system.
✓
Answer
The unit of energy is SI system is Joule and that is in the CGS system is erg.
Dimensional formula of energy $=\left[ M ^1 L^2 T^{-2}\right]$
Here, $a=1, b=2, c=-2$
S.I. System
$M _1=1 kg$
$L _1=1 m$
$T _1=1 s$
$n _1=1$ Joule
C.G.S. System
$M _2=1 gm$
$L _2=1 cm$
$T _2=1 s$
$n _2=$ ?
$\begin{aligned}
n_2 & =n_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c \\
& =1\left[\frac{1 kg}{1 g}\right]^1\left[\frac{1 m}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1\left[\frac{1000 g}{1 g}\right]^1\left[\frac{100 cm}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1 \times 10^3 \times\left(10^2\right)^2=10^3 \times 10^4=10^7
\end{aligned}$
Hence, 1 Joule $=10^7$ erg.
Dimensional formula of energy $=\left[ M ^1 L^2 T^{-2}\right]$
Here, $a=1, b=2, c=-2$
S.I. System
$M _1=1 kg$
$L _1=1 m$
$T _1=1 s$
$n _1=1$ Joule
C.G.S. System
$M _2=1 gm$
$L _2=1 cm$
$T _2=1 s$
$n _2=$ ?
$\begin{aligned}
n_2 & =n_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c \\
& =1\left[\frac{1 kg}{1 g}\right]^1\left[\frac{1 m}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1\left[\frac{1000 g}{1 g}\right]^1\left[\frac{100 cm}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1 \times 10^3 \times\left(10^2\right)^2=10^3 \times 10^4=10^7
\end{aligned}$
Hence, 1 Joule $=10^7$ erg.
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